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The Coulomb-gauge vector potential of a uniformly moving point charge is obtained by calculating the gauge function for the transformation between the Lorenz and Coulomb gauges. The expression obtained for the difference between the vector…
The main purposes of this paper are (i) to illustrate explicitly by a number of examples the gauge functions chi(x, t) whose spatial and temporal derivatives transform one set of electromagnetic potentials into another equivalent set; and…
Vector and scalar potentials are used for convenience in solving boundary value problems involving electromagnetic (EM) fields. The potentials are made unique by choosing a non-unique gauge relationship. The most commonly used gauges are…
In light of a recent direct experimental confirmation of a Lorentz contraction of Coulomb field (an electric field of a point charge in a uniform motion), we revisit some common confusions related to it, to be mindful of in teaching the…
In the classical electrodynamics, different gauges, i.e. connections between the electromagnetic potentials, are used. Some of these are quite specific and intended for calculations in special systems (absence of free charges, etc.). All of…
The instantaneous nature of the potentials of the Coulomb gauge is clarified and a concise derivation is given of the vector potential of the Coulomb gauge expressed in terms of the instantaneous magnetic field.
The Maxwell field equations relative to a uniformly accelerated frame, and the variational principle from which they are obtained, are formulated in terms of the technique of geometrical gauge invariant potentials. They refer to the…
If potential energy is the timelike component of a four-vector, then there must be a corresponding spacelike part which would logically be called the potential momentum. The potential four-momentum consisting of the potential momentum and…
Gauge transformations are potential transformations that leave only specific Maxwell fields invariant. To reveal more, I develop Lorenz field equations with full Maxwell form for nongauge, sans gauge function, transformations yielding…
We generalize the derivation of electromagnetic fields of a charged particle moving with a constant acceleration [1] to a variable acceleration (piecewise constants) over a small finite time interval using Coulomb's law, relativistic…
The Maxwell's electromagnetic equations are isomorphic to the motion equation of a linear elastic continuum which is hard to compression though liable to shear deformation. The Coulomb gauge expresses the medium incompressibility. The…
We examine physical aspects for the electric version of a recently proposed logarithmic electrodynamics, for which the electric field of a point-like charge is finite at the origin. It is shown that this electrodynamics displays the vacuum…
The question of an instantaneous action (A M Stewart 2003 Eur. J. Phys. 24, 519) can be approached in a systematic way applying the Helmhotz vector decomposition theorem to a two-parameter Lorenz-like gauge. We thus show that only the…
There is a simple formula for the gauge function of the transformation from the Lorenz gauge to the Coulomb gauge, valid under a condition that is satisfied by some charge densities employed in the literature. An equation for the gauge…
This paper presents a simple and systematic method to show how the potentials in the Lorentz, Coulomb, Kirchhoff, velocity and temporal gauges yield the same retarded electric and magnetic fields. The method appropriately uses the dynamical…
We investigate the coupling of the electromagnetic sources (charge and current densities) to the scalar and vector potentials in classical electrodynamics, using Green function techniques. As is well known, the scalar potential shows an…
Two results support the idea that the scalar and vector potentials in the Lorenz gauge can be considered to be physical quantities: (i) they separately satisfy the properties of causality and propagation at the speed of light and not imply…
Modern undergraduate textbooks in electricity and magnetism typically focus on a force representation of electrodynamics with an emphasis on Maxwell's Equations and the Lorentz Force Law. The vector potential $\mathbf{A}$ and scalar…
Although gauge invariance preserves the values of physical observables, a gauge transformation can introduce important alterations of physical interpretations. To understand this, it is first shown that a gauge transformation is not, in…
It is shown that the well-known procedure for proving the equivalence of the expressions for the electric field calculated using the Lorentz and Coulomb gauges is incorrect. The difference between the two gauges is due to the difference in…